Abstract

Generally, the analysis of corneal topography involves fitting the raw data to a parametric geometric model that includes a regular basis surface, plus some sort of polynomial expansion to adjust the more irregular residual component. So far, these parametric models have been used in their canonical form, ignoring that the observation (keratometric) coordinate system is different from corneal axes of symmetry. Here we propose, instead, to use the canonical form when the topography is referenced to the intrinsic corneal system of coordinates, defined by its principal axes of symmetry. This idea is implemented using the general expression of an ellipsoid to fit the raw data given by the instrument. Then, the position and orientation of the three orthogonal semiaxes of the ellipsoid, which define the intrinsic Cartesian system of coordinates for normal corneas, can be identified by passing to the canonical form, by standard linear algebra. This model has been first validated experimentally obtaining significantly lower values for rms fitting error as compared with previous standard models: spherical, conical, and biconical. The fitting residual was then adjusted by a Zernike polynomial expansion. The topographies of 123 corneas were analyzed obtaining their radii of curvature, conic constants, Zernike coefficients, and the direction and position of the optical axis of the ellipsoid. The results were compared with those obtained using the standard models. The general ellipsoid model provides more negative values for the conic constants and lower apex radii (more prolate shapes) than the standard models applied to the same data. If the data are analyzed using standard models, the resulting mean shape of the cornea is consistent with previous studies, but when using the ellipsoid model we find new interesting features: The mean cornea is a more prolate ellipsoid (apical power 50D), the direction of the optical axis is about 2.3° nasal, and the residual term shows three Zernike coefficients significantly higher than zero (third-order trefoil and fourth- and sixth-order spherical). These three nonzero Zernike coefficients are responsible for most of the higher-order aberrations of the average cornea. Finally, we propose and implement a simple method for three-dimensional registration of corneal topographies, passing from the general to the canonical form of the ellipsoid.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Le Grand and S. G. El Hage, Physiological Optics (Springer-Verlag, 1980).
  2. A. Ivanoff, Les Aberrations de l'Oeil. Leur Role dans l'Accommodation, Éditions de la Revue d'Optique Théorique et Instrumentale (Institut d'Optique, Paris, 1953).
  3. M. Millodot and J. Sivak, "Contribution of the cornea and lens to the spherical aberration of the eye," Vision Res. 19, 685-687 (1979).
    [Crossref] [PubMed]
  4. W. Lotmar, "Theoretical eye model with aspheric surfaces," J. Opt. Soc. Am. 61, 1522-1529 (1971).
    [Crossref]
  5. D. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).
  6. J. Schwiegerling and R. Snyder, "Custom photorefractive keratectomy ablations for the correction of spherical and cylindrical refractive error and higher-order aberration," J. Opt. Soc. Am. A 15, 2572-2579 (1998).
    [Crossref]
  7. H. Burek and W. A. Douthwaite, "Mathematical models of the general corneal surface," Ophthalmic Physiol. Opt. 13, 68-72 (1993).
    [Crossref] [PubMed]
  8. P. R. Preussner, J. Wahl, and C. Kramann, "Cornea model," J. Cataract Refractive Surg. 29, 471-477 (2003).
    [Crossref]
  9. M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, "A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern," Optom. Vision Sci. 72, 821-827 (1995).
    [Crossref]
  10. J. Schwiegerling, J. Greivenkamp, and J. Miller, "Representation of videokeratoscopic height data with Zernike polynomials," J. Opt. Soc. Am. A 12, 2105-2113 (1995).
    [Crossref]
  11. D. R. Iskander, M. J. Collins, and B. Davis, "Optimal modeling of corneal surfaces with Zernike polynomials," IEEE Trans. Biomed. Eng. 48, 87-95 (2001).
    [Crossref] [PubMed]
  12. R. P. Hemenger, A. Tomlinson, and K. Oliver, "Corneal optics from videokeratographs," Ophthalmic Physiol. Opt. 15, 63-68 (1995).
    [Crossref] [PubMed]
  13. J. Schwiegerling and J. E. Greivenkamp, "Using corneal height maps and polynomial decomposition to determine corneal aberrations," Optom. Vision Sci. 74, 906-916 (1997).
    [Crossref]
  14. P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
    [Crossref]
  15. S. Barbero, S. Marcos, J. Merayo-Lloves, and E. Moreno-Barriuso, "Validation of the estimation of corneal aberrations from videokeratography: A test on keratoconus eyes," J. Cataract Refractive Surg. 28, 1594-1603 (2002).
    [Crossref]
  16. P. M. Kiely, G. Smith, and L. G. Carney, "The mean shape of the human cornea," Opt. Acta 29, 1027-1040 (1982).
    [Crossref]
  17. M. Guillon, D. P. M. Lidon, and C. Wilson, "Corneal topography: a clinical model," Ophthalmic Physiol. Opt. 6, 47-56 (1986).
    [Crossref] [PubMed]
  18. A. Tomlinson and C. Schwartz, "The position of the corneal apex in the normal eye," Am. J. Optom. Physiol. Opt. 56, 236-240 (1979).
    [PubMed]
  19. R. B. Mandell, C. S. Chiang, and S. A. Klein, "Location of the major corneal reference points," Optom. Vision Sci. 72, 776-784 (1995).
    [Crossref]
  20. J. Y. Wang, D. A. Rice, and S. D. Klyce, "Analysis of the effects of astigmatism and misalignment on corneal surface reconstruction from photokeratoscopic data," Refract. Corneal Surg. 7, 129-140 (1991).
    [PubMed]
  21. R. Navarro, L. González, and J. L. Hernández, "Prediction of optical aberrations by personalized eye models," presented at the second Physiological Optics Topical Meeting of the European Optical Society, Granada, Spain, September 2004.
  22. L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and Its Applications, V.Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (2000) (Optical Society of America, 2000), pp. 232-244.
  23. A. Guirao and P. Artal, "Corneal wave aberration from videokeratography: accuracy and limitations of the procedure," J. Opt. Soc. Am. A 17, 955-965 (2000).
    [Crossref]
  24. T. O. Salmon and L. N. Thibos, "Videokeratoscope-line-of-sight misalignment and its effect on measurements of corneal and internal ocular aberrations," J. Opt. Soc. Am. A 19, 657-669 (2002).
    [Crossref]
  25. M. K. Smolek and S. D. Klyce, "Zernike polynomial fitting fails to represent all visually significant corneal aberrations," Invest. Ophthalmol. Visual Sci. 44, 4676-4681 (2003).
    [Crossref]

2003 (2)

P. R. Preussner, J. Wahl, and C. Kramann, "Cornea model," J. Cataract Refractive Surg. 29, 471-477 (2003).
[Crossref]

M. K. Smolek and S. D. Klyce, "Zernike polynomial fitting fails to represent all visually significant corneal aberrations," Invest. Ophthalmol. Visual Sci. 44, 4676-4681 (2003).
[Crossref]

2002 (2)

T. O. Salmon and L. N. Thibos, "Videokeratoscope-line-of-sight misalignment and its effect on measurements of corneal and internal ocular aberrations," J. Opt. Soc. Am. A 19, 657-669 (2002).
[Crossref]

S. Barbero, S. Marcos, J. Merayo-Lloves, and E. Moreno-Barriuso, "Validation of the estimation of corneal aberrations from videokeratography: A test on keratoconus eyes," J. Cataract Refractive Surg. 28, 1594-1603 (2002).
[Crossref]

2001 (2)

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
[Crossref]

D. R. Iskander, M. J. Collins, and B. Davis, "Optimal modeling of corneal surfaces with Zernike polynomials," IEEE Trans. Biomed. Eng. 48, 87-95 (2001).
[Crossref] [PubMed]

2000 (1)

1998 (1)

1997 (1)

J. Schwiegerling and J. E. Greivenkamp, "Using corneal height maps and polynomial decomposition to determine corneal aberrations," Optom. Vision Sci. 74, 906-916 (1997).
[Crossref]

1995 (4)

R. B. Mandell, C. S. Chiang, and S. A. Klein, "Location of the major corneal reference points," Optom. Vision Sci. 72, 776-784 (1995).
[Crossref]

R. P. Hemenger, A. Tomlinson, and K. Oliver, "Corneal optics from videokeratographs," Ophthalmic Physiol. Opt. 15, 63-68 (1995).
[Crossref] [PubMed]

M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, "A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern," Optom. Vision Sci. 72, 821-827 (1995).
[Crossref]

J. Schwiegerling, J. Greivenkamp, and J. Miller, "Representation of videokeratoscopic height data with Zernike polynomials," J. Opt. Soc. Am. A 12, 2105-2113 (1995).
[Crossref]

1993 (1)

H. Burek and W. A. Douthwaite, "Mathematical models of the general corneal surface," Ophthalmic Physiol. Opt. 13, 68-72 (1993).
[Crossref] [PubMed]

1991 (1)

J. Y. Wang, D. A. Rice, and S. D. Klyce, "Analysis of the effects of astigmatism and misalignment on corneal surface reconstruction from photokeratoscopic data," Refract. Corneal Surg. 7, 129-140 (1991).
[PubMed]

1986 (1)

M. Guillon, D. P. M. Lidon, and C. Wilson, "Corneal topography: a clinical model," Ophthalmic Physiol. Opt. 6, 47-56 (1986).
[Crossref] [PubMed]

1982 (1)

P. M. Kiely, G. Smith, and L. G. Carney, "The mean shape of the human cornea," Opt. Acta 29, 1027-1040 (1982).
[Crossref]

1979 (2)

A. Tomlinson and C. Schwartz, "The position of the corneal apex in the normal eye," Am. J. Optom. Physiol. Opt. 56, 236-240 (1979).
[PubMed]

M. Millodot and J. Sivak, "Contribution of the cornea and lens to the spherical aberration of the eye," Vision Res. 19, 685-687 (1979).
[Crossref] [PubMed]

1971 (1)

Applegate, R. A.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and Its Applications, V.Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (2000) (Optical Society of America, 2000), pp. 232-244.

Artal, P.

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
[Crossref]

A. Guirao and P. Artal, "Corneal wave aberration from videokeratography: accuracy and limitations of the procedure," J. Opt. Soc. Am. A 17, 955-965 (2000).
[Crossref]

Atchison, D.

D. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

Barbero, S.

S. Barbero, S. Marcos, J. Merayo-Lloves, and E. Moreno-Barriuso, "Validation of the estimation of corneal aberrations from videokeratography: A test on keratoconus eyes," J. Cataract Refractive Surg. 28, 1594-1603 (2002).
[Crossref]

Barsky, B. A.

M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, "A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern," Optom. Vision Sci. 72, 821-827 (1995).
[Crossref]

Berrio, E.

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
[Crossref]

Burek, H.

H. Burek and W. A. Douthwaite, "Mathematical models of the general corneal surface," Ophthalmic Physiol. Opt. 13, 68-72 (1993).
[Crossref] [PubMed]

Carney, L. G.

P. M. Kiely, G. Smith, and L. G. Carney, "The mean shape of the human cornea," Opt. Acta 29, 1027-1040 (1982).
[Crossref]

Chiang, C. S.

R. B. Mandell, C. S. Chiang, and S. A. Klein, "Location of the major corneal reference points," Optom. Vision Sci. 72, 776-784 (1995).
[Crossref]

Collins, M. J.

D. R. Iskander, M. J. Collins, and B. Davis, "Optimal modeling of corneal surfaces with Zernike polynomials," IEEE Trans. Biomed. Eng. 48, 87-95 (2001).
[Crossref] [PubMed]

Davis, B.

D. R. Iskander, M. J. Collins, and B. Davis, "Optimal modeling of corneal surfaces with Zernike polynomials," IEEE Trans. Biomed. Eng. 48, 87-95 (2001).
[Crossref] [PubMed]

Douthwaite, W. A.

H. Burek and W. A. Douthwaite, "Mathematical models of the general corneal surface," Ophthalmic Physiol. Opt. 13, 68-72 (1993).
[Crossref] [PubMed]

El Hage, S. G.

Y. Le Grand and S. G. El Hage, Physiological Optics (Springer-Verlag, 1980).

González, L.

R. Navarro, L. González, and J. L. Hernández, "Prediction of optical aberrations by personalized eye models," presented at the second Physiological Optics Topical Meeting of the European Optical Society, Granada, Spain, September 2004.

Greivenkamp, J.

Greivenkamp, J. E.

J. Schwiegerling and J. E. Greivenkamp, "Using corneal height maps and polynomial decomposition to determine corneal aberrations," Optom. Vision Sci. 74, 906-916 (1997).
[Crossref]

Guillon, M.

M. Guillon, D. P. M. Lidon, and C. Wilson, "Corneal topography: a clinical model," Ophthalmic Physiol. Opt. 6, 47-56 (1986).
[Crossref] [PubMed]

Guirao, A.

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
[Crossref]

A. Guirao and P. Artal, "Corneal wave aberration from videokeratography: accuracy and limitations of the procedure," J. Opt. Soc. Am. A 17, 955-965 (2000).
[Crossref]

Halstead, M. A.

M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, "A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern," Optom. Vision Sci. 72, 821-827 (1995).
[Crossref]

Hemenger, R. P.

R. P. Hemenger, A. Tomlinson, and K. Oliver, "Corneal optics from videokeratographs," Ophthalmic Physiol. Opt. 15, 63-68 (1995).
[Crossref] [PubMed]

Hernández, J. L.

R. Navarro, L. González, and J. L. Hernández, "Prediction of optical aberrations by personalized eye models," presented at the second Physiological Optics Topical Meeting of the European Optical Society, Granada, Spain, September 2004.

Iskander, D. R.

D. R. Iskander, M. J. Collins, and B. Davis, "Optimal modeling of corneal surfaces with Zernike polynomials," IEEE Trans. Biomed. Eng. 48, 87-95 (2001).
[Crossref] [PubMed]

Ivanoff, A.

A. Ivanoff, Les Aberrations de l'Oeil. Leur Role dans l'Accommodation, Éditions de la Revue d'Optique Théorique et Instrumentale (Institut d'Optique, Paris, 1953).

Kiely, P. M.

P. M. Kiely, G. Smith, and L. G. Carney, "The mean shape of the human cornea," Opt. Acta 29, 1027-1040 (1982).
[Crossref]

Klein, S. A.

R. B. Mandell, C. S. Chiang, and S. A. Klein, "Location of the major corneal reference points," Optom. Vision Sci. 72, 776-784 (1995).
[Crossref]

M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, "A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern," Optom. Vision Sci. 72, 821-827 (1995).
[Crossref]

Klyce, S. D.

M. K. Smolek and S. D. Klyce, "Zernike polynomial fitting fails to represent all visually significant corneal aberrations," Invest. Ophthalmol. Visual Sci. 44, 4676-4681 (2003).
[Crossref]

J. Y. Wang, D. A. Rice, and S. D. Klyce, "Analysis of the effects of astigmatism and misalignment on corneal surface reconstruction from photokeratoscopic data," Refract. Corneal Surg. 7, 129-140 (1991).
[PubMed]

Kramann, C.

P. R. Preussner, J. Wahl, and C. Kramann, "Cornea model," J. Cataract Refractive Surg. 29, 471-477 (2003).
[Crossref]

Le Grand, Y.

Y. Le Grand and S. G. El Hage, Physiological Optics (Springer-Verlag, 1980).

Lidon, D. P. M.

M. Guillon, D. P. M. Lidon, and C. Wilson, "Corneal topography: a clinical model," Ophthalmic Physiol. Opt. 6, 47-56 (1986).
[Crossref] [PubMed]

Lotmar, W.

Mandell, R. B.

M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, "A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern," Optom. Vision Sci. 72, 821-827 (1995).
[Crossref]

R. B. Mandell, C. S. Chiang, and S. A. Klein, "Location of the major corneal reference points," Optom. Vision Sci. 72, 776-784 (1995).
[Crossref]

Marcos, S.

S. Barbero, S. Marcos, J. Merayo-Lloves, and E. Moreno-Barriuso, "Validation of the estimation of corneal aberrations from videokeratography: A test on keratoconus eyes," J. Cataract Refractive Surg. 28, 1594-1603 (2002).
[Crossref]

Merayo-Lloves, J.

S. Barbero, S. Marcos, J. Merayo-Lloves, and E. Moreno-Barriuso, "Validation of the estimation of corneal aberrations from videokeratography: A test on keratoconus eyes," J. Cataract Refractive Surg. 28, 1594-1603 (2002).
[Crossref]

Miller, J.

Millodot, M.

M. Millodot and J. Sivak, "Contribution of the cornea and lens to the spherical aberration of the eye," Vision Res. 19, 685-687 (1979).
[Crossref] [PubMed]

Moreno-Barriuso, E.

S. Barbero, S. Marcos, J. Merayo-Lloves, and E. Moreno-Barriuso, "Validation of the estimation of corneal aberrations from videokeratography: A test on keratoconus eyes," J. Cataract Refractive Surg. 28, 1594-1603 (2002).
[Crossref]

Navarro, R.

R. Navarro, L. González, and J. L. Hernández, "Prediction of optical aberrations by personalized eye models," presented at the second Physiological Optics Topical Meeting of the European Optical Society, Granada, Spain, September 2004.

Oliver, K.

R. P. Hemenger, A. Tomlinson, and K. Oliver, "Corneal optics from videokeratographs," Ophthalmic Physiol. Opt. 15, 63-68 (1995).
[Crossref] [PubMed]

Preussner, P. R.

P. R. Preussner, J. Wahl, and C. Kramann, "Cornea model," J. Cataract Refractive Surg. 29, 471-477 (2003).
[Crossref]

Rice, D. A.

J. Y. Wang, D. A. Rice, and S. D. Klyce, "Analysis of the effects of astigmatism and misalignment on corneal surface reconstruction from photokeratoscopic data," Refract. Corneal Surg. 7, 129-140 (1991).
[PubMed]

Salmon, T. O.

Schwartz, C.

A. Tomlinson and C. Schwartz, "The position of the corneal apex in the normal eye," Am. J. Optom. Physiol. Opt. 56, 236-240 (1979).
[PubMed]

Schwiegerling, J.

Schwiegerling, J. T.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and Its Applications, V.Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (2000) (Optical Society of America, 2000), pp. 232-244.

Sivak, J.

M. Millodot and J. Sivak, "Contribution of the cornea and lens to the spherical aberration of the eye," Vision Res. 19, 685-687 (1979).
[Crossref] [PubMed]

Smith, G.

P. M. Kiely, G. Smith, and L. G. Carney, "The mean shape of the human cornea," Opt. Acta 29, 1027-1040 (1982).
[Crossref]

D. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

Smolek, M. K.

M. K. Smolek and S. D. Klyce, "Zernike polynomial fitting fails to represent all visually significant corneal aberrations," Invest. Ophthalmol. Visual Sci. 44, 4676-4681 (2003).
[Crossref]

Snyder, R.

Thibos, L. N.

T. O. Salmon and L. N. Thibos, "Videokeratoscope-line-of-sight misalignment and its effect on measurements of corneal and internal ocular aberrations," J. Opt. Soc. Am. A 19, 657-669 (2002).
[Crossref]

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and Its Applications, V.Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (2000) (Optical Society of America, 2000), pp. 232-244.

Tomlinson, A.

R. P. Hemenger, A. Tomlinson, and K. Oliver, "Corneal optics from videokeratographs," Ophthalmic Physiol. Opt. 15, 63-68 (1995).
[Crossref] [PubMed]

A. Tomlinson and C. Schwartz, "The position of the corneal apex in the normal eye," Am. J. Optom. Physiol. Opt. 56, 236-240 (1979).
[PubMed]

Wahl, J.

P. R. Preussner, J. Wahl, and C. Kramann, "Cornea model," J. Cataract Refractive Surg. 29, 471-477 (2003).
[Crossref]

Wang, J. Y.

J. Y. Wang, D. A. Rice, and S. D. Klyce, "Analysis of the effects of astigmatism and misalignment on corneal surface reconstruction from photokeratoscopic data," Refract. Corneal Surg. 7, 129-140 (1991).
[PubMed]

Webb, R.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and Its Applications, V.Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (2000) (Optical Society of America, 2000), pp. 232-244.

Williams, D. R.

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
[Crossref]

Wilson, C.

M. Guillon, D. P. M. Lidon, and C. Wilson, "Corneal topography: a clinical model," Ophthalmic Physiol. Opt. 6, 47-56 (1986).
[Crossref] [PubMed]

Am. J. Optom. Physiol. Opt. (1)

A. Tomlinson and C. Schwartz, "The position of the corneal apex in the normal eye," Am. J. Optom. Physiol. Opt. 56, 236-240 (1979).
[PubMed]

IEEE Trans. Biomed. Eng. (1)

D. R. Iskander, M. J. Collins, and B. Davis, "Optimal modeling of corneal surfaces with Zernike polynomials," IEEE Trans. Biomed. Eng. 48, 87-95 (2001).
[Crossref] [PubMed]

Invest. Ophthalmol. Visual Sci. (1)

M. K. Smolek and S. D. Klyce, "Zernike polynomial fitting fails to represent all visually significant corneal aberrations," Invest. Ophthalmol. Visual Sci. 44, 4676-4681 (2003).
[Crossref]

J. Cataract Refractive Surg. (2)

S. Barbero, S. Marcos, J. Merayo-Lloves, and E. Moreno-Barriuso, "Validation of the estimation of corneal aberrations from videokeratography: A test on keratoconus eyes," J. Cataract Refractive Surg. 28, 1594-1603 (2002).
[Crossref]

P. R. Preussner, J. Wahl, and C. Kramann, "Cornea model," J. Cataract Refractive Surg. 29, 471-477 (2003).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Vision (1)

P. Artal, A. Guirao, E. Berrio, and D. R. Williams, "Compensation of corneal aberrations by the internal optics in the human eye," J. Vision 1, 1-8 (2001).
[Crossref]

Ophthalmic Physiol. Opt. (3)

M. Guillon, D. P. M. Lidon, and C. Wilson, "Corneal topography: a clinical model," Ophthalmic Physiol. Opt. 6, 47-56 (1986).
[Crossref] [PubMed]

R. P. Hemenger, A. Tomlinson, and K. Oliver, "Corneal optics from videokeratographs," Ophthalmic Physiol. Opt. 15, 63-68 (1995).
[Crossref] [PubMed]

H. Burek and W. A. Douthwaite, "Mathematical models of the general corneal surface," Ophthalmic Physiol. Opt. 13, 68-72 (1993).
[Crossref] [PubMed]

Opt. Acta (1)

P. M. Kiely, G. Smith, and L. G. Carney, "The mean shape of the human cornea," Opt. Acta 29, 1027-1040 (1982).
[Crossref]

Optom. Vision Sci. (3)

J. Schwiegerling and J. E. Greivenkamp, "Using corneal height maps and polynomial decomposition to determine corneal aberrations," Optom. Vision Sci. 74, 906-916 (1997).
[Crossref]

M. A. Halstead, B. A. Barsky, S. A. Klein, and R. B. Mandell, "A spline surface algorithm for reconstruction of corneal topography from a videokeratographic reflection pattern," Optom. Vision Sci. 72, 821-827 (1995).
[Crossref]

R. B. Mandell, C. S. Chiang, and S. A. Klein, "Location of the major corneal reference points," Optom. Vision Sci. 72, 776-784 (1995).
[Crossref]

Refract. Corneal Surg. (1)

J. Y. Wang, D. A. Rice, and S. D. Klyce, "Analysis of the effects of astigmatism and misalignment on corneal surface reconstruction from photokeratoscopic data," Refract. Corneal Surg. 7, 129-140 (1991).
[PubMed]

Vision Res. (1)

M. Millodot and J. Sivak, "Contribution of the cornea and lens to the spherical aberration of the eye," Vision Res. 19, 685-687 (1979).
[Crossref] [PubMed]

Other (5)

D. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, 2000).

Y. Le Grand and S. G. El Hage, Physiological Optics (Springer-Verlag, 1980).

A. Ivanoff, Les Aberrations de l'Oeil. Leur Role dans l'Accommodation, Éditions de la Revue d'Optique Théorique et Instrumentale (Institut d'Optique, Paris, 1953).

R. Navarro, L. González, and J. L. Hernández, "Prediction of optical aberrations by personalized eye models," presented at the second Physiological Optics Topical Meeting of the European Optical Society, Granada, Spain, September 2004.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, "Standards for reporting the optical aberrations of eyes," in Vision Science and Its Applications, V.Lakshminarayanan, ed., Vol. 35 of OSA Trends in Optics and Photonics Series (2000) (Optical Society of America, 2000), pp. 232-244.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

RMS fit errors obtained using the four corneal models for 123 corneas: sphere, conic, biconic, and general ellipsoid.

Fig. 2
Fig. 2

Two examples of corneal topographies; the upper panels correspond to an example of a high fit error, the lower panels to the opposite case. From left to right we see the raw topography, the ellipsoid resulting from the data fit, the residual difference, and the Zernike fit to the residual.

Fig. 3
Fig. 3

Optical axes obtained for 106 corneas. Upper panel: x and y angles between the optical and keratometric axes. Lower panel: location of the corneal axis intercept (apex). Error bars are indicated for the 22 eyes for which we had nine topographies each.

Fig. 4
Fig. 4

Radii of curvature obtained using the four models for the 106 corneas: *, sphere; ◇ conic, ◻ biconic, ● general ellipsoid. Error bars are shown for 22 eyes, general ellipsoid model. Linear regression lines are also indicated for the biconic (dashed) and ellipsoid (solid) models.

Fig. 5
Fig. 5

Conic constants for the ◇ conic, ◻ biconic, ● general ellipsoid models. Error bars are given for 22 corneas, ellipsoid model.

Fig. 6
Fig. 6

Average and standard deviation (error bars) of the Zernike coefficients obtained by fitting the residual for the 106 corneas. The ordering of the polynomials is that of the Optical Society of America Standards (Ref. [22]); coefficient 0 corresponds to piston.

Fig. 7
Fig. 7

Zernike coefficients and error bars (variability) for the two examples in Fig. 2, corresponding to two opposite cases of high and low magnitudes of the coefficients.

Fig. 8
Fig. 8

Topography of the mean cornea. Top left, average topography; top right, average Zernike coefficients; lower panels, average ellipsoid for left and right corneas, respectively. For the overall average, x was replaced with x for OD. Note the different scale used for the residual.

Fig. 9
Fig. 9

High-order aberrations of the mean cornea computed for a 6 mm pupil and 550 nm wavelength: left, mean cornea with incident wavefront aligned with the keratometric axis; center, same but for the ellipsoid alone; right, ellipsoid and wavefront aligned with the corneal optical axis.

Fig. 10
Fig. 10

Expected improvement in measurement error by 3D registration of the raw topographies: white bars, standard deviations after direct averaging versus black bars, those obtained after 3D registration.

Tables (1)

Tables Icon

Table 1 Parameters of the Mean Cornea in the Different Representations a

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

z S ( x , y ) = b ( x , y ) + r ( x , y ) ,
r ( x , y ) = k c k P k ,
z = c x x 2 + c y y 2 1 + 1 ( 1 + Q x ) c x 2 x 2 ( 1 + Q y ) c y 2 y 2 .
x 2 a 2 + y 2 b 2 + z 2 c 2 = 1 .
a 11 x 2 + a 22 y 2 + a 33 z 2 + a 12 x y + a 13 x z + a 23 y z + a 1 x + a 2 y + a 3 z + a 0 = 0 .
X = R ( X 0 + X 1 ) ,
R x ( α ) = [ 1 0 0 0 cos α sin α 0 sin α cos α ] ,
R y ( β ) = [ cos β 0 sin β 0 1 0 sin β 0 cos β ] ,
R z ( γ ) = [ cos γ sin γ 0 sin γ cos γ 0 0 0 1 ] .
X 1 T Λ X 1 = 1 , with Λ = [ 1 a 2 0 0 0 1 b 2 0 0 0 1 c 2 ] ,
C ( X T A X + X T L + a 0 ) = 0 ,
with A = 1 C [ a 11 a 12 2 a 13 2 a 12 2 a 22 a 23 2 a 13 2 a 23 2 a 23 ] = R Λ R T ,
L = 1 C ( a 1 a 2 a 3 ) = 2 X 0 T Λ R T , a 0 = X 0 T Λ X 0 1 .
X 0 T = 1 2 L U T Λ 1 ;
C = X 0 T Λ X 0 α 0 .
a = C λ 1 , b = C λ 2 , c = C λ 3 .

Metrics